HalfLife of Barium137m
Introduction:
One of the characteristics often used to describe radioisotopes is halflife. Halflife is the time required for half of a radioisotope to disintegrate. This value is a constant and is not affected by changes such as temperature or pressure. Halflives of radioisotopes can vary from fractions of a second to millions of years. In order to determine the halflife of a sample, the actual number of radioactive atoms need not be known. The activity of a sample measured by a GM tube and scaler is proportional to the number of radioactive atoms in that sample. When the measured activity of a sample reaches a value equal to one half the original activity, half of that sample has undergone radioactive decay. The period of time required for this process is the halflife of the sample.
In this experiment, the halflife of Ba137m will be determined. A halflife value can be determined in several different ways. These values can be found by estimation of the data, graphically, and mathematically. By comparing the results with the accepted value, the percent error in each method can be calculated.
The source of the Ba137m is a mini generator or "cow." The Ba137m is formed by the disintegration of Cs137. The “m” in Ba137m means that the nucleus of the newly formed Barium atom is in an excited state. The excited nucleus emits energy and becomes stable.
Cs137 ® Ba137m + _{1}e^{0}
Ba137m ® Ba137 + _{0}g^{0}
The mini generator contains an ionexchange resin that releases Ba^{++} ions but retains Cs^{+} ions when a solution is passed through the column. This process is sometimes called "milking the cow."
Purpose:
The purpose of this experiment is to determine the halflife of Ba137m by several methods and to determine the percent error for each determination.
Equipment:
GM tube and scaler eluting solution
Cs  Ba mini generator graph paper (linear and/or semilog)
planchet stop watch
Safety:
Wear gloves and an apron when handling an open source. Special care must be taken not to spill the solution. Leave the planchet in the sample holder when finished. The instructor will dispose of the sample at the end of the lab.
Procedure:
1. Plug in the scaler and allow it to warm up for a few minutes. Set the high voltage to 750.
2. With no sample in the sample holder, take a oneminute background count. Record the value in the data table. Repeat for a second oneminute background count.
3. Obtain a sample containing Ba137m in a planchet and place it on the highest shelf possible in the sample holder. Set the timer to the manual setting.
4. Beginning on the minute take 10 second readings every 30 seconds for ten minutes. This sounds more complicated than it is. The scaler will be on for ten seconds, then it will be off for twenty seconds. Use this time to record data and reset the scaler. Begin the next reading when the second hand reaches thirty, and continue to read on the minute and halfminute for 10 minutes.
5. Have the instructor remove the sample holder with the planchet. Be sure no radioactive sources are near the scaler.
6. When all samples have been collected, take another one minute background reading and record the information on the data table.
7. Convert the readings for ten seconds to counts per minute by multiplying by six. Subtract background for those values that are less than 1000 cpm. These values constitute your corrected cpm.
8. Plot the corrected cpm on linear and/or semilog graph paper. The corrected cpm should be plotted on the yaxis and the time on the xaxis. Use the “plotat” for the time values. These are the time values for the midpoint of each counting interval.
Data Table:
Background count __________ __________ __________
Measure at

Counts 10 s

Counts per min

Corrected cpm

Plot at (s)

0:00  0:10




5

0:30  0:40




35

1:00  1:10




65

1:30 1:40




95

2:00  2:10




125

2:30  2:40




155

3:00  3:10




185

3:30  3:40




215

4:00  4:10




245

4:30  4:40




275

5:00  5:10




305

5:30  5:40




335

6:00  6:10




365

6:30  6:40




395

7:00  7:10




425

7:30  7:40




455

8:00  8:10




485

8:30  8:40




515

9:00  9:10




545

9:30  9:40




575

10:00  10:10




605

Calculations:
1. One method to estimate a value for halflife is to examine the data. From the data table, select two values (corrected cpm). One value should be twice as large as the other. Take the difference between these values. This is an approximate halflife. Calculate percent error for this determination.
count rate_{1} = __________
count rate_{2} = __________
time difference = half life = __________
percent error = __________
2. A second method of determining halflife is to use a graph of the data. From the graph, choose two count rates of which one is twice as large as the other. List these count rates and the time difference between these points. The time difference is the half life. Calculate the percent error for determining halflife by this method.
count rate_{1} = __________
count rate_{2} = __________
time difference = half life = __________
percent error = __________
3. The last method to find halflife is a mathematical method. Find the cpm for 65 and 575 seconds from your graph. The bestfit line is a better representation of the data than the individual data points. Use the formula below to calculate the halflife and then calculate the percent error for this determination. Show work.
t_{1} = 65 seconds count rate_{1} = ____________
t_{2} = 575 seconds count rate_{2} = ____________
t_{1/2}
Questions:
1. Why does a researcher often take a background reading before and after an experiment where an open source has been used?
2. What would happen if the halflife data were plotted at the end of the counting interval instead of at the middle, as was suggested in this experiment?
3. What would happen to the value for your halflife if corrections for background were not made?
HALFLIFE OF BARIUM 137m
Teacher Notes
Standards Met:
3.4.12.A – Apply concepts about the structure and properties of matter.

Classify and describe, in equation form, types of chemical and nuclear reactions.

Explain how radioactive isotopes that are subject to decay can be used to estimate the age of materials.

Apply the conservation of energy concept to fields as diverse as mechanics, nuclear particles and studies of the origin of the universe.

Apply the predictability of nuclear decay to estimate the age of materials that contain radioactive isotopes.
3.7.10.B – Apply appropriate instruments and apparatus to examine a variety of objects and processes.

Describe and use appropriate instruments to gather and analyze data.
3.1.10.B – Describe concepts of models as a way to predict and understand science and technology.

Apply mathematical models to science and technology.
3.1.12.E – Evaluate change in nature, physical systems and man made systems.

Evaluate fundamental science and technology concepts and their development over time.
3.7.12.A – Apply advanced tools, materials and techniques to answer complex questions.

Demonstrate the safe use of complex tools and machines within their specifications.

Evaluate and use technological resources to solve complex multistep problems.
Lab Time: 45 minutes
Answers to Questions:
1. Why does a researcher often take a background reading before and after an experiment where an open source has been used?
A background reading is often taken at the beginning and end of a lab to determine if the operator of the scaler has contaminated the scaler with a radioactive material. If the setup is clean at the end of an experiment the background should be the same as at the beginning.
2. What would happen if the halflife data were plotted at the end of the counting interval instead of at the middle, as was suggested in this experiment?
The value for the halflife would not change. The line would be shifted slightly to the right, but the slope and therefore the halflife would remain the same.
3. What would happen to the value for the halflife if corrections for background were not made?
The end of the graph would be higher. This would reduce the slope and give longer values for the halflife.
Considerations:
The Ba/Cs mini generator used in this experiment poses little risk. Due to the short halflife of the isotope generated, the activity should drop to background within an hour. If this does not occur, some of the Cs137 may be leaking through. Under normal circumstances the used solution can be washed down the drain.
The halflife of Barium137m is approximately 153 seconds. Different references will give slightly different halflife values.
Instruct the students in how to find halflife from a graph. If students are careful, percent errors of less than 510% are not uncommon.
HalfLife Computer Simulation
To prepare students for a halflife experiment, a program called Decay available from Seraphim Software may be useful. This program may be obtained free or at the cost of a disk through the Spectroscopy Society of Pittsburgh.
The program simulates nuclear decay on the screen and then prints out a set of data for the students. Each group of students receives a different set of data. The students may then plot the data and obtain halflife values. No time units are provided. The students may make up their own units as well as name the "isotope" being studied.
Last updated 1102.
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